本原向量的$p$ -adic方向
$p$-adic Directions of Primitive Vectors
摘要：
Linnik型问题涉及单位球面上整点的投影随着其范数的增加而分布，以及对这种现象的不同推广。我们的工作解决了这种类型的问题：我们证明了均匀分布的原始$\mathbb{Z}^{2}$点的$p$ -进单位球的投影，因为他们的（真正的）规范趋于无穷大。证明是通过计算半单$S$ -算术群的格点。
英文摘要：
Linnik type problems concern the distribution of projections of integral points on the unit sphere as their norm increases, and different generalizations of this phenomenon. Our work addresses a question of this type: we prove the uniform distribution of the projections of primitive $\mathbb{Z}^{2}$ points in the $p$-adic unit sphere, as their (real) norm tends to infinity. The proof is via counting lattice points in semi-simple $S$-arithmetic groups.
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